4 Answers
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In general, there's no price difference for checking in at the airport or via any other means, although there can be price differences for other services (eg baggage charges) depending on where you pay for them - more on that below.

There are, however, a small number of exceptions in the form of Low-Cost Carriers (LCCs) who are interested in squeezing every last possible cent out of you to make up for the low initial ticket price. Ryanair is the best known offender here, charging £60/€60 per person (depending on the departure location) to print/reprint your boarding pass at the airport. Spirit Airlines in the US also charges, but the fees are a little more sensible at $2-$5 per person. The airline should list these fees on their website, so if you're flying a LCC it's certainly worth checking beforehand.

Where many airlines do charge differently depending on where you pay for it is for check baggage - paying in advance will often be cheaper than paying at the airport. Normally you can still pay the baggage fees online and then check-in at the airport for no additional fee - as long as you've paid the checked bag fee in advance.

Spirit is (again!) one of the best example of this - from November, taking a carry-on bag onto one of their flights will cost you $35 if paid in advance, $50 if done at check-in, and $100 if done at the gate! Most other carries are not quite so high, but most LCC and even many normal carriers will have different prices for checked bags at the airport vs in advance.

A few low-cost airlines charge extra for checking in at the airport. Most airlines let you print your boarding pass at a machine. The airlines that charge for airport checkin usually let you check in online further in advance, typically a couple of weeks (non-low-cost airlines often open checkin only one or two days before the flight).

Ryanair charges a whooping €60 or £60 for printing a boarding card at the airport. (It's not extortion if it's mentioned in their terms of service.) Mind you, they charge €6 or £6 if you check in online (which may well make their prices false advertising in some locales). Easyjet doesn't currently charge for printing a boarding pass at a machine (they do, however, add a £9 “booking fee” to all fares except the top flexible fare, and charge extra if you pay by credit card).

This is true, I came over this piece of information myself when I had stood in line to check in at the Kuala Lumpur (KUL) LCCT (Low Cost Carrier Terminal) with the airline Air Asia. If this is restricted to only Air Asia or the same applies to other carriers at the LCCT I am not sure.

I do not remember how much the "fine" was, but it was not dismissively little for us traveling on a budget.

To be fair, you are informed when booking with Air Asia that extra charges might occur during check in when flying through an airport with such a system. However during this leg of the trip I was not the one booking the ticket and had not received that information. This piece of information is easily lost when trying to go through their very complex booking system.

I believe that there are other airports that also have the same warning flag raised when booking through the Air Asia website, but I am not sure. And when I last checked it said something along the lines of "...charges might occur...". As in they don't explicitly say that it will cost extra to not do the online check in, but might.

As far as I can tell it does not matter if it is domestic or international, if you have to check in it applies to you.

EDIT: This was in April of 2012.

EDIT 2: Air Asia provides online check in through website (printer needed I believe), through your phone (smartphone with display to show barcode) and machines at the terminals it flies to. The machines will want the confirmation paper with the barcode that you received in your email. I believe you are able to type in said barcode/booking information in to the machine as well if you don't have it printed.